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My worry has definitely faded over the years as I have watched my children become capable of finding needed information themselves, of supporting their own interests. For example, The Girl loves animals. She searched out David Attenborough documentaries, found books at the library, delved into all of it and taught herself more about mammals, dinosaurs, and sea creatures, by the age of 13, than even I know at the advanced age of 43. The Boy knows cars from a distance—old and new—just from their silhouette. As for history and science, we have watched documentaries, read books, talked through the scientific method. We've studied art casually hung on the door of the fridge, listened to music that spans centuries, and enjoyed many period films.
I've seen over the years that if you teach a child to read [and do math] and you model for them how to find information, they become capable of doing just that, finding the information they need.
As for knowing every detail, I can honestly say that never in my life, since childhood, has anyone quizzed me about which president served when, or the order of the the periodic table of elements. To function, as a teacher at the college level mind you, I don't need to know who Marie Antoinette's sisters and brothers were, or in what year a specific battle took place.
I do think children, and adults, should be aware of the general flow of history and the basic tenets of science. They should have a basic familiarity with names, countries, events, and such. They should know who Napoleon was, or Hitler, and why we celebrate every July 4th. They should know where major countries are, how weather and seasons work, the basics of physics, and how plants grow.
There are so many things overlooked when we focus on strictly an academic approach. As well as being able to write a decent essay and understand geometric proofs, they should be able to balance a checkbook, change a tire, cook a meal, sew on a button, do their own laundry. They should be able to follow their interests, and above all, learn how to find information. I'm not advocating a hands-off approach with learning, rather that perhaps priorities need to be reviewed and shifted on an occasional basis.
If my children graduate able to communicate easily both verbally and in writing, able to understand higher math (at least to a certain point, that being whatever level it is they need), can generally take care of themselves (life skills), and are able to search out the next pieces they need, I think I'll be comfortable. Learning doesn't stop when I stop explicitly teaching them. They will continue learning throughout their lifetimes, and surely that will allow them to fill in some "gaps". They'll leap, with my support and the support of others, across any abyss, or chasm.
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